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Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects. (English) Zbl 1207.34104

From the text: We discuss a class of stochastic differential delay equations with nonlinear impulsive effects of the form

dy(t)={-a 1 (t)y(t)-a 2 (t)y(t-τ(t))}dt+{-b 1 (t)y(t)-b 2 (t)y(t-τ(t))]dw(t),tt k ,y(t k + )-y(t k )=I k (y(t k )),t=t k ,k,

where I k C(,), k are continuous functions with I k (0)0.

The purpose of this paper is to build a bridge between the given stochastic impulsive delay equation and a corresponding stochastic delay equation without impulsive effects, and to establish some stability criteria for these systems. Furthermore, the desired conditions are given explicitly.

34K50Stochastic functional-differential equations
34K20Stability theory of functional-differential equations
34K45Functional-differential equations with impulses
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